# Verification and limitations

The five-page manuscript proves the canonical independent-set bound for every finite simple r-uniform 2-regular hypergraph, for all integers r >= 2. Its proof is analytic. The general source conjecture for degree d >= 3, all equality cases, and the precise finite-n maximum outside the sharp divisibility remain outside its scope.

The self-audit checks dual simplicity, entropy direction and normalization, extreme-point support, strict chord reduction, inducedness in the ambient graph, boundary aggregation, the explicit perfect matching in the doubled graph, non-circular use of the matching case, and the exact rational spectral comparison.

Normal and optimized Python runs agree exactly. The suite checks 4,742 labelled regular multigraphs in stated exhaustive small domains and 400 seeded examples with two independent edge-cover counts; 84,525 chord reductions; 2,016 pair identities; 800 closed-cycle trace cases; and coefficientwise polynomial identities. No floating-point comparison decides a mathematical verdict. These finite regressions are not a formal proof of the arbitrary-size theorem.

The edge-cover dual and regional method of Sarantis--Tetali--Zheng are credited. Three primary PDFs and fifteen full-page visual reviews are retained locally; third-party PDF files are not redistributed. The source archive includes original reproducibility code and the written audit.

This is an AI-assisted, self-audited, unrefereed preprint. No independent expert review, proof-assistant certification or absolute priority determination is claimed.